Police told AFP an investigation is ongoing into Tuesday's early morning attack, but would not comment on the group's online posting.
The Games were held on stolen indigenous lands in Vancouver, the anarchists said. "The Vancouver Olympic Games are over, but a torch is still burning."
"G8 and G20 leaders and bankers are meeting (next month) in Huntsville and Toronto to make decisions that will further their policies of exploitation of people and the environment," the group said. "We will be there."
An online video posted by the group, which can be viewed on YouTube, shows the fireball bursting through the bank's windows in a blinding flash.
Police said witnesses saw "three or four males running from the scene" in Ottawa's smart Glebe neighborhood "and leaving the area in an SUV (sport utility) vehicle a short time before the fire was reported."
No one was injured, but the storefront was gutted and damage was "extensive," police said, adding in a statement that there were no further descriptions of the vehicle nor the suspects.
Some 4,000 Royal Canadian Mounted Police officers will be on hand to provide security for the G8 and G20 summits from June 25 to 27.